The California Department of Motor Vehicles has accused the company of misrepresenting its driver-assistance technology, which could affect the company's ability to sell cars in the state.
The agency said that it was false for the company to claim that its vehicles were autonomously driving. If the agency succeeds in getting their complaints heard by the Office of Administrative Hearings, they could lose their licenses to make and sell cars in California.
The agency said in its complaints that the statements made by the company were false or misleading.
The Los Angeles Times reported earlier on the agency's complaints, which are separate from its review of the car company.
There was no response from Musk or the company lawyer on Friday evening.
In marketing materials on its website, the company said its driver-assistance technology was able to conduct trips with no action required by the person in the driver's seat. The agency said that the claim and others were false and misleading.
Since 2015, the company's cars can be steered, brake and accelerate on their own with the help of the autopilot system. The company requires drivers to keep their hands on the wheel and take control of the car in the event of a malfunction.
It is named after aviation systems that allow planes to fly themselves in ideal conditions. If drivers don't keep a hand on the wheel the car will disengage.
The features for the typical buyer are not very significant. The car will stop at a red light if the driver doesn't intervene, but it won't progress after a green light if the driver doesn't intervene.
Mr. Musk said in May that 100,000 Full Self-Driving buyers had access to a test version of the service that could navigate city streets more extensively. Full Self-Driving will be available to a million car owners by the end of the year, according to him.
Mr. Musk said at the end of 2015 that he would have his cars driving themselves within two years. He has claimed that it was just a year or two away.
He said there were so many false dawns with self- driving. You think you have a solution to the problem, but then you hit a ceiling.
The National Highway Traffic Safety Administration became aware of 35 crashes involving the system and nine of them resulted in death. There are 830,000 vehicles sold in the United States and it will look at full self- driving and autopilot.
The California Department of Motor Vehicles has until next Friday to give a response to the allegations.